DEMAND ELASTICITY Overview Context: Product manager wants to - - PowerPoint PPT Presentation

DEMAND ELASTICITY

Overview

• Context: Product manager wants to estimate impact of price

change on sales (quantity and revenue). How sensitive is demand to price? How important is the pricing of competing products?

• Concepts: demand elasticity, cross-elasticity
• Economic principle: sometimes reducing price attracts many more

customers, sometimes very few

How sensitive is demand to price changes?

• Example 1: world oil demand decreases by 1.3 million barrels a

day when price increases from $50 to $60 dollars per barrel. Would you consider the demand for oil very sensitive or not very sensitive to price?

• Example 2: demand for sugar in Europe decreases by 1 million

tones per day when average retail price increases from e.80 to e.90 per kilo. Can you compare the demand for sugar in Europe to the worldwide demand for oil?

• Problem: by measuring the slope of the demand curve, we are

stuck with units: barrels, dollars, kilos, euros, and so on.

Demand elasticity: definition

✏ ≡

d q q d p p

= d q d p p q = d log q d log p

Demand elasticity: definition

✏ ≡

d q q d p p

= d q d p p q = d log q d log p ≈

∆ q q ∆ p p

=

% ∆ quantity % ∆ price

Demand elasticity: definition

✏ ≡

d q q d p p

= d q d p p q = d log q d log p ≈

∆ q q ∆ p p

=

% ∆ quantity % ∆ price

≈

∆ log quantity ∆ log price

Demand elasticity: notes

• Elasticity and slope are not the same
• Elasticity is independent of units
• Knowing price change, quantity change may be estimated based
• n elasticity:

∆ q q ≈ ✏ ∆ p p

Examples

Product Elasticity Milk

• 0.5

Cigarettes

• 0.5

Beer

• 0.8

Apples

• 1.3

US luxury cars in US

• 1.9

Foreign luxury cars in US

• 2.8

Elasticity illustrated: linear demand

p q

✏ = 0 |✏| < 1 |✏| = 1 |✏| > 1 ✏ = −∞

Elasticity illustrated: constant elasticity

p q

✏ = −∞ |✏| > 1 |✏| < 1 ✏ = 0

Elasticity, price, and revenue

Revenue ≡ R = p × q. Therefore: ∆ R R = ∆ (p × q) (p × q) ≈ q ∆ p + p ∆ q (p × q) = ∆ p p + ∆ q q = ∆ p p + ✏ ∆ p p = ∆ p p (1 + ✏) If price falls, then:

• Revenue rises if ✏ < −1 (that is, |✏| > 1)
• Revenue falls if ✏ > −1 (that is, |✏| < 1)
• Revenue is unchanged if ✏ = −1

Elasticity, price, and revenue

Examples: for a 1% decrease in price,

• Cigarettes: revenue falls approx 0.5% = −.1%×(1+(−.5))
• U.S. luxury cars: revenue rises approx 0.9%
• Foreign luxury cars: revenue rises approx 1.8%

Revenue change from price decrease

∆p ∆q p q E1 E2 q p

Loss L = q (−∆ p), Gain G = p ∆ q G > L iff p ∆ q > q (−∆ p) iff

∆ q ∆ p p q < −1

Cross-price elasticity

• Idea: How sensitive is demand for your product to prices of

competing products? Answer: Cross-price elasticity. ✏ij =

d qi qi d pj pj

• Jargon:

− If ✏ij > 0, we say i and j are substitutes − If ✏ij < 0, we say i and j are complements − If ✏ij = 0, we say i and j are independent

• Examples?

Income elasticity

• Idea: How sensitive is demand for your product to consumer

income? Answer: income elasticity. ✏y =

d q q d y y

• Jargon:

− Inferior good: ✏y < 0 − Normal good: ✏y > 0 − Necessity: 0 < ✏y < 1 − Luxury: ✏y > 1

• Examples?

Example: U.S. gasoline demand (cont)

Example: gasoline demand

• Based on U.S. data from 1953–2004,

ln q = −16.1 − 0.03 ln p + 1.17 ln y − 0.33 ln c + 0.85 ln n

where q: gasoline consumption p: gasoline price y: per capita income c: price of cars n: population

• What is the gasoline demand elasticity? Income elasticity? Cross

price elasticity w.r.t. cars? How do you classify the good “gasoline”?

Example: gasoline demand

• From 1953 to 2004, p, y, c and n increased at the following

annual rates: 3.9, 2.2, 2.0, 1.2%. How much do you expect demand to have grown?

• Recall that d z

z = ✏zx d x x , for any z and x. Hence,

∆ q q = −.03 × 3.9% + 1.17 × 2.2% − 0.33 × 2 + .85 × 1.2% = −.117% + 2.574% − 0.66% + 1.02% = 2.817%

• Note: actual growth rate was 2.7%

Takeaways

• The elasticity (of demand) measures sensitivity of buyers to

changes in price

• It’s useful for computing impact of price changes on quantity and

revenue

• Cross-price and income elasticities measure sensitivity to other

factors